Modelling and Simulating Random Phenomena
Computer simulation has become an essential tool in many areas of human endeavour, including science, engineering, management and entertainment. However, specific difficulties arise when the systems to be simulated contain random components. Take the example of a business that does not know ahead of time what the demand for a particular product will be, or that of a communication or transportation network where there is no advance information on traffic volume at each point in the network. In order to use simulations to study and potentially optimize management of systems such as these, the first step required is to build mathematical models that accurately represent the behavioural aspects of interest-for example, quality of service in a network or revenues and expenses of a business. It is then possible to generate a computer simulation of changes in the models and optimize their parameters using specially designed algorithms or heuristics.
Computer generators of random values are a key component of any simulation involving a random variable. They are also an essential feature of computer games, gambling machines (lottery terminals), and communications security systems (cryptology). Quality criteria for generators vary with the application concerned-hence the need to study them from various standpoints and build several types.
An expert in the simulation of stochastic systems, Pierre L'Écuyer will devote part of his time as chairholder to developing and studying effective methods of simulating systems with random components and to optimizing systems of this kind by means of simulation-based methods. He will focus on the application of such methods in a variety of fields, including finance, risk management, communications, and management of business operations.
He will also continue his research on the design, mathematical analysis, effective use and statistical testing of generators of random values for a variety of applications. He is recognized as a world authority in this field. At the same time, he wilI study quasi-Monte Carlo methods for large-scale digital integration and the close links between these methods and the construction of high-quality generators of random values.
Dr. L'Écuyer will examine the mathematical and the theoretical aspects of these questions, including algorithm convergence analysis and mathematical analysis of the structure of points produced by generators or by digital integration methods, and the practical aspects, such as software implementation and experimentation.